Disjoint Union Metric Spaces

By : Meenakshi

Page No: 81-87

Abstract
From the given metrics di on disjoint sets Xi , i = 1,2,3..., we define a new metric d on their union X so that it becomes a metric space. Further, we relate open spheres of the given sets to the open spheres of X so as to determine the structure of an open set in X. Finally, by using the inclusion mappings, we observe that the disjoint union topology of the topologies generated by di ’s on Xi ’s is the same as the topology generated by metric d on X.

Author :
Meenakshi : Research Scholar, Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005